Let U = {1, 2, 3, ..., 36} and A = {x ∈ U : x is a perfect square}. What is n(Aᶜ)?
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Answer and explanation
Correct answer: 30
The universal set U contains all integers from 1 through 36, so n(U) = 36. The perfect squares in this range are 1, 4, 9, 16, 25, and 36; hence n(A) = 6. The complement contains every element of U that is not a perfect square. Therefore, n(Aᶜ) = n(U) − n(A) = 36 − 6 = 30, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
30
Why is this the correct answer?
The universal set U contains all integers from 1 through 36, so n(U) = 36. The perfect squares in this range are 1, 4, 9, 16, 25, and 36; hence n(A) = 6. The complement contains every element of U that is not a perfect square. Therefore, n(Aᶜ) = n(U) − n(A) = 36 − 6 = 30, so option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
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